Prove that the area of a right angled triangle of given hypotenuse is maximum when the

triangle is isosceles

Let *h* be the hypotenuse of the right-angles triangle, and let *x* be it altitude.

Then,

Base of the triangle

Let A be the area of the triangle. Then,

For maximum or minimum, we have

Now,

Thus, A is maximum when

Hence, A maximum when the triangle is isosceles.

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